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UA AEM 201 - Numerical Methods
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AEM 201 1st Edition Lecture 5PREVIOUS LECTUREI. Summarizing Quantitative DataII. Summary of Tabular and Graphical DisplaysIII. Simultaneous Display of Multiple Variables-Two Qualitative VariablesIV. Simultaneous Display of Multiple Variables-One Qualitative One Quantitative VariableV. Simultaneous Display of Multiple Variables-Two Quantitative VariablesCURRENT LECTUREI. Simultaneous Display of Multiple Variable-Two Quantitative VariablesII. Best Practices In Creating Effective Visual DisplaysIII. Numerical Methods-Measures of Location-Qualitative DataIV. Numerical Methods-Measures of Location-Quantitative DataSIMULTANEOUS DISPLAY OF MULTIPLE VARIABLES-TWO QUANTITATIVEVARIABLES- Star Glyph: graphical simultaneous presentation of the values of more than two variables on a coordinate system (use when comparing values for more than two quantitative variables across individual observations)o A little difficult to make direct comparisonso If there are too many dimensions, it can become too difficult to read. Eight is a good number of maximum dimensions to haveo Sometimes people fill their star glyphs You can hang additional info on this display like putting a name on it ect.- Data Dashboard: a set of visual displays that organizes and presents information that is used in an integrated manner to monitor the performance of a company or organizationo To be useful and effective, a data dashboard must be easy to read, understand, and interpreto Drilling Down: moving from higher level summary information to a lower level of detailed information to learn more about what is behind the summary informationBEST PRACTICES IN CREATING EFFECTIVE VISUAL DISPLAYSThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.- Portray data in graphs or tables when the display reveals patterns in the data that are otherwise difficult to detect- Whenever appropriate, each graph in this presentation has:o A titleo A label on the x-axiso A label on the y-axiso Labels for intermittent values in the x-axiso Labels for intermittent values on the y-axis- Appropriate labeling is an important part of creating complete and accurate graphical and tabular displays-graphical and tabular displays are not complete (or correct) until they are documented with appropriate and meaningful labeling- Keep in mind that a good display consists of complex ideas communicated with clarity, precision, and efficiency- Considero Available technologyo The message to be conveyedo The audience- Label important events or points in the data- Never use:o 3D effectso Luminescent shading or patterns- Eliminate all superfluous graphical elements- Maximize the Data-Ink Ratio-proportion of a graphic’s ink devoted to the non-redundant display of information- Use animation and sound ONLY to call attention to important points to be made by the display- Appropriate labeling is an important part of creating complete accurate graphical and tabular displays-graphical and tabular displays are not complete (or correct) until they are documented with appropriate and meaningful labelingNUMERICAL METHODS:MEASURES OF LOCATION-QUALITATIVE DATA- Proportion: relative frequency that a characteristic occurs in a data set. o Population Proportion calculated as: P= (# of population elements with characteristics)/(total # of elements in population (N)) =(# of sample observations with characteristic)/(total # of observations in sample (n))- a characteristic of a population is a parameter-it can only be collected by a census- (sample) is our best guess and P (population)- The more samples taken, the closer the average gets to P- Note that 0 is less than p, and p is less than 1. 0 is also less than , and is less than 1NUMERICAL METHODS: MEASURES OF LOCATION-QUANTITATIVEDATA- Midrange: value half the distance between the minimum and maximum values in the data seto Calculated as: Minimum value+[(maximum value-minimum value)/2] X1+[(XN-X1)/2] (population) X1+[(Xn-X1)/2] (sample)- Data must be in an array 1st because we need to know the minimum and maximum- Midrange is easy to calculate and explain- The midrange can be misleading because of extremes can heavily influence the midrange value and may not represent the data. We only use two data values (the extremes) and they are each weighted and half. Not very robust with respect to extremes or outliers- Arithmetic Mean: (known as mean or average) measure of central location calculated by summing all values in data set and dividing by the number of summed valueso population meano =sample meanxx- is a guess of what xx Does not mean that x bar is the population. It is our best guess of what mu is.- Mean is most used but can be misleading but not as misleading as midrange- You can give data less weight by collecting more data- The mean is still sensitive to extremes- The arithmetic mean acts like the fulcrum of a see-saw masses are placed on the lever at different locations (distances from the fulcrum in each direction). If the torque (mass*distance from the fulcrum) is on both sides of the fulcrum will be equal- If you take each number in the data set and subtract it by the mean and add all of the numbers together, you will get zero EVERY time- Trimmed (Arithmetic) Mean: arithmetic mean that results after most extreme (smallest and largest) T% of values have been eliminated from the data. o j=(T/200)*N Has to be the largest integer that does not exceed (T/200)*N This is the numbers of values that must be trimmed from each end- Trimmed means are used in the Olympics scoring to minimize effects of extreme ratings caused by biased judges- You do not decide to trim after seeing the data. If you trim after you could be biasing data- We are concentrating weight on data and the middle and taking weights away from the extremes- Median: value in the middle of the data array. Often denoted as Mdfor a population and md for a sample (can be looked at as an extremely trimmed mean)- If the data set has an odd number of observations, the median is the (n+1)/2th (or middle) value of the data arrayo This is for location of the data- If the data set has even number of observations median is (nth)/(2+1)- Extreme Value Elimination Method: put data in an array and systematically eliminate the most extreme values remaining until you are left with only one or two values-the mean of


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UA AEM 201 - Numerical Methods

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